I think the most damage is to thier head. Most riders spur spur spur then they haul back on the reins and then as the horse is trying to slow down they spur spur spur again. The worst part of barrel racing is putting up with barrel racers. Even bull riders won't put up with some of it.
I agree very much with Kevin on this.
Also I would like to add that most people believe that your horse can just up and become a barrel racer by running a pattern.
You need a solid foundation and grasp of not only the physical but mental and emotional effects on the horse.
Not only does your horse need to be able to rate and move individual parts of its body almost without notice, he must be able to enter and exit the arena with a cool focused head.
Very little training for barrels should be done near a barrel pattern or even an arena.
To keep a horse mentally sound and emotionally cool, it is best to spend 98% of your time away from an arena and pattern. Lots of field and trail work are great for a barrel horse, it teaches him balance.
Your horse must have the heart to run, otherwise he can become very burnt out very quickly. If you feel you have to whip and kick him to get him to do his best he does not need to be racing.
I could go on and on and on about why most people fail at barrel racing(failure in my book is not laying the proper foundations that make the horse wear unnecessarily both mentally and physically, it is not understanding the concepts required for a happy healthy barrel horse, it is selfishly wanting to follow your "barrel dreams" with little regard to the well being and suitability of your horse), and would be happy to if you would like to pm me.